Outage, Symbol Error Probability, and Rate of RIS-Assisted MIMO Systems With Phase Errors

This work provides a comprehensive performance analysis of a reconfigurable intelligent surface (RIS)-assisted multiple-input multiple-output (MIMO) communication system in the presence of phase errors. We first derive the exact expressions for the first and second moments of the maximum signal-to-noise ratio at the receiver. We then use these moments to obtain highly accurate and insightful expressions for the outage probability, average symbol error probability (SEP), and ergodic rate (ER) for various phase error distributions, leveraging the moment-matching approach. Furthermore, we present closed-form asymptotic expressions for these performance metrics. The derived expressions are then leveraged to gain important insights into the impact of phase errors on the scaling laws of diversity order, coding gain, and ER. The numerical results show that the presence of phase errors can significantly degrade the system’s diversity order and coding gain. Specifically, we show that, in the absence of phase errors, the diversity order scales linearly with the number of RIS elements, while the diversity order reduces to unity in the presence of uniformly distributed phase errors. Finally, the analytical findings are demonstrated through extensive simulation results.